Information on Result #2266306
Linear OA(3200, 19747, F3, 31) (dual of [19747, 19547, 32]-code), using 3 times code embedding in larger space based on linear OA(3197, 19744, F3, 31) (dual of [19744, 19547, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(22) [i] based on
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3136, 19683, F3, 23) (dual of [19683, 19547, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(316, 61, F3, 7) (dual of [61, 45, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3200, 10940, F3, 2, 31) (dual of [(10940, 2), 21680, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3200, 10940, F3, 3, 31) (dual of [(10940, 3), 32620, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3200, 10940, F3, 4, 31) (dual of [(10940, 4), 43560, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3200, 10940, F3, 5, 31) (dual of [(10940, 5), 54500, 32]-NRT-code) | [i] | ||
| 5 | Digital (169, 200, 10940)-net over F3 | [i] | ||